Lattice methods for algebraic modular forms on classical groups

TL;DR

This paper applies lattice-based computational methods to determine systems of Hecke eigenvalues for definite classical algebraic groups, advancing the computational tools in the field.

Contribution

It introduces the use of Kneser's neighbor method and isometry testing for lattices to compute Hecke eigenvalues on classical groups.

Findings

Successful computation of Hecke eigenvalues for specific classical groups

Demonstration of lattice methods as effective tools in algebraic modular forms

Potential for extending computational techniques to broader classes of groups

Abstract

We use Kneser's neighbor method and isometry testing for lattices due to Plesken and Souveigner to compute systems of Hecke eigenvalues associated to definite forms of classical reductive algebraic groups.